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Totally disconnected locally compact (tdlc) groups are of interest for two reasons: on one hand, important classes of tdlc groups arise in combinatorial geometry, number theory and algebra and, on the other, an essential part of the task of describing the structure of general locally compact groups is understanding the totally disconnected case. Interest in these groups is currently very high because of the rapid progress being made with the general theory.
Advances in our understanding of the structure of tdlc groups are being made through three loosely related approaches:
• the scale, a positive integer-valued function defined on automorphisms of tdlc groups that relates to eigenvalues in algebraic representations of these groups and to translation distance in geometric representations;
• the structure lattice of locally normal subgroups of a tdlc group, which gives rise to a local theory underpinning a typology of simple tdlc groups; and
• a decomposition theory for tdlc groups that exploits methods for gauging their size and breaks a given group into smaller, and often simple, pieces.
These approaches are developing a conceptual framework that promises to support a comprehensive description of tdlc groups. At the same time, more examples filling out this framework are being found. There is still some way to go before this description could be regarded as complete however.
The current interest perhaps prompted the Oberwolfach Forschungsinstitut to ask P.-E. Caprace and N. Monod to organise the Arbeitsgemeinschaft Totally Disconnected Groups in October, 2014, with the aim of bringing together these approaches and the researchers and students involved. Lectures surveyed the background for the study of tdlc groups and introduced the main ideas and most recent developments in the three approaches described above. These notes, which cover the lectures as well as including a couple of other invited surveys, thus provide a valuable review of the current state of knowledge. It is to be hoped that they will serve as a reference for further work that goes toward completing the description of totally disconnected, locally compact groups.
The illegal killing and taking of wild birds remains a major threat on a global scale. However, there are few quantitative data on the species affected and countries involved. We quantified the scale and scope of this issue in Northern and Central Europe and the Caucasus, using a diverse range of data sources and incorporating expert knowledge. The issue was reported to be widespread across the region and affects almost all countries/territories assessed. We estimated that 0.4–2.1 million birds per year may be killed/taken illegally in the region. The highest estimate of illegal killing in the region was for Azerbaijan (0.2-1.0 million birds per year). Out of the 20 worst locations identified, 13 were located in the Caucasus. Birds were reported to be illegally killed/taken primarily for sport and food in the Caucasus and for sport and predator/pest control in both Northern and Central Europe. All of the 28 countries assessed are parties to the Bern Convention and 19 are also European Union Member States. There are specific initiatives under both these policy instruments to tackle this threat, yet our data showed that illegal killing and taking is still occurring and is not restricted to Mediterranean European countries. Markedly increased effort is required to ensure that existing legislation is adequately implemented and complied with/enforced on the ground. Our study also highlighted the paucity of data on illegal killing and taking of birds in the region. It is a priority, identified by relevant initiatives under the Bern Convention and the European Union, to implement systematic monitoring of illegal killing and taking and to collate robust data, allowing stakeholders to set priorities, track trends and monitor the effectiveness of responses.
Objectives: Careful characterization of how functional decline co-evolves with cognitive decline in older adults has yet to be well described. Most models of neurodegenerative disease postulate that cognitive decline predates and potentially leads to declines in everyday functional abilities; however, there is mounting evidence that subtle decline in instrumental activities of daily living (IADLs) may be detectable in older individuals who are still cognitively normal. Methods: The present study examines how the relationship between change in cognition and change in IADLs are best characterized among older adults who participated in the ACTIVE trial. Neuropsychological and IADL data were analyzed for 2802 older adults who were cognitively normal at study baseline and followed for up to 10 years. Results: Findings demonstrate that subtle, self-perceived difficulties in performing IADLs preceded and predicted subsequent declines on cognitive tests of memory, reasoning, and speed of processing. Conclusions: Findings are consistent with a growing body of literature suggesting that subjective changes in everyday abilities can be associated with more precipitous decline on objective cognitive measures and the development of mild cognitive impairment and dementia. (JINS, 2018, 24, 104–112)
be a totally disconnected, locally compact group. A closed subgroup of
is locally normal if its normalizer is open in
. We begin an investigation of the structure of the family of closed locally normal subgroups of
. Modulo commensurability, this family forms a modular lattice
, called the structure lattice of
. We show that
admits a canonical maximal quotient
for which the quasicentre and the abelian locally normal subgroups are trivial. In this situation
has a canonical subset called the centralizer lattice, forming a Boolean algebra whose elements correspond to centralizers of locally normal subgroups. If
is second-countable and acts faithfully on its centralizer lattice, we show that the topology of
is determined by its algebraic structure (and thus invariant by every abstract group automorphism), and also that the action on the Stone space of the centralizer lattice is universal for a class of actions on profinite spaces. Most of the material is developed in the more general framework of Hecke pairs.
We use the structure lattice, introduced in Part I, to undertake a systematic study of the class
consisting of compactly generated, topologically simple, totally disconnected locally compact groups that are nondiscrete. Given
, we show that compact open subgroups of
involve finitely many isomorphism types of composition factors, and do not have any soluble normal subgroup other than the trivial one. By results of Part I, this implies that the centralizer lattice and local decomposition lattice of
are Boolean algebras. We show that the
-action on the Stone space of those Boolean algebras is minimal, strongly proximal, and microsupported. Building upon those results, we obtain partial answers to the following key problems: Are all groups in
abstractly simple? Can a group in
be amenable? Can a group in
be such that the contraction groups of all of its elements are trivial?
Between 1984 and 1995 over 450 organic samples were collected from monuments built during the Old and Middle Kingdoms. The most suitable samples were selected for dating. The purpose was to establish a radiocarbon chronology with samples from secure context and collected with the careful techniques required for 14C samples. This chronology is compared to the historical chronology established by reconstructing written documentation.
14C ages were determined on samples of foraminifera separated from cores from three areas of the tropical Pacific (East Pacific Rise, Oontong Java Plateau, and South China Sea). Analyses were made on four planktonic species and on mixed benthics. The purpose of the multiple analysis on planktonic species is to assess the importance of artifacts resulting from the bioturbation-abundance change couple, from the bioturbation-partial dissolution couple and from redeposition by bottom currents. The goal is to use the benthic-planktonic age difference as a means of establishing changes in deep sea ventilation rate over the past 25,000 years. Results of a part of this work are presented in this paper.
A computer program for convenient calibration of radiocarbon dates has been developed. The program has a simple user interface, which includes pull-down menus, windows and mouse support. All important information, such as calibration curves, probability density function and results, in text form, are displayed on the screen and easily can be rearranged by the user. Two versions of CalibETH, one for an IBM-PC and one for the Macintosh, are available. CalibETH runs under the graphics interface, GEM, from Digital Research, on an IBM PC.
The name Dead Sea Scrolls refers to some 1200 manuscripts found in caves in the hills on the western shore of the Dead Sea during the last 45 years. They range in size from small fragments to complete books from the holy scriptures (the Old Testament). The manuscripts also include uncanonized sectarian books, letters and commercial documents, written on papyrus and parchment. In only a few cases, direct information on the date of writing was found in the scrolls. In all other cases, the dating is based on indirect archaeological and paleographical evidence. To check this evidence, radiocarbon ages of 14 selected scrolls were determined using accelerator mass spectrometry. The calibrated radiocarbon ages agree well, except in one case, with the paleographic estimates or the specific dates noted on the scrolls.
Results of 14C/12C ratio measurements on CO2 extracted from air bubbles in polar ice are presented. The samples investigated originate from the Dye 3, South Greenland, deep ice core and span approximately the last 10,000 years. The results are calibrated with tree-ring records. The 14C ages are compared with information obtained from seasonal variations of ice-core parameters and rheologic model calculation.
Radiocarbon ages on handpicked foraminifera from deep-sea cores are revealing that areas of rapid sediment accumulation are in some cases subject to hiatuses, reworking and perhaps secondary calcite deposition. We present here an extreme example of the impacts of such disturbances. The message is that if precise chronologies or meaningful benthic planktic age differences are to be obtained, then it is essential to document the reliability of radiocarbon ages by making both comparisons between coexisting species of planktonic foraminifera and detailed down-core sequences of measurements.
A technique for 14C measurement of small volume (0.5L) oceanic water samples by Accelerator Mass Spectrometry (AMS) is described. Samples were taken from a CTD/rosette system used for standard hydrographic work. After CO2 extraction and target preparation, the samples were measured at the Zürich tandem accelerator facility. On the basis of 14C data from samples collected on a station in the northern Weddell Sea, the precision of the measurements is estimated to ca ±8‰. The error in the present AMS results is dominated by the statistical error in 14C detection. From results of duplicate targets, it is concluded that a precision of ±5° can be reached. The 14C data are discussed in relation to the Weddell Sea hydrography.
Sherds can be dated by four independent methods: 14C beta counting on associated material, accelerator mass spectrometry on carbon traces on and within the sherd, thermoluminescence studies on minerals within the sherd, and stylistic form. Age analyses of materials and sherds from several sites are shown in this work. Each technique has its own frequently encountered non-laboratory sources of error. A combination of at least two independent techniques is indispensable for the highest level of confidence.
Radiocarbon ages determined by the AMS method on hand-picked foraminifera shells are reported. The results allow estimates of the ventilation rate of the deep Atlantic and Pacific Oceans during glacial time. They also extend our knowledge of the chronology of events associated with the transition from full glacial conditions ca 15,000 years ago to full interglacial conditions ca 8000 years ago. This and the previous lists (Broecker et al 1988c) contain all the results obtained as part of this program through the fall of 1989.
The main purpose of this work is to reconstruct the atmospheric Δ 14C in the glacial-postglacial transition, 14,000 – 10,000 BP, a range not covered by the tree-ring calibration curve. We measured 14C/12C ratios on series of terrestrial macrofossils from sediments of two Swiss lakes. We selected exclusively plant remains of recognizable terrestrial origin that are not affected by hard water and thus reflect atmospheric 14C concentration. Due to the scarcity of such material, we used accelerator mass spectroscopy. Cores of two lakes were measured to eliminate local effects and to check the reproducibility of results. This required a reliable, 14C-independent correlation of the cores, obtained through local pollen zone boundaries 14C ages were obtained as a function of the depth in the cores. If sedimentation rates are known ages can be converted into Δ 14C values. We also attempted estimating sedimentation rates; calculations are based on the Swedish varve chronology. Results were combined to form an entire data set. The Δ 14C curve shows an increase with time during the Allerød and decreases during Preboreal and Bølling periods. Probabilities for these 14C variations are discussed.
During the last three years the ETH-EN-tandem accelerator facility has been adapted for the quantitative determination of the rare isotopes 14C and 10Be in mg samples. The goal of this project is to routinely achieve a 1% accuracy when measuring 14C/12C ratios with a minimum expenditure of human resources and beam time. The concept is similar to that proposed by Purser and Henley (1978). The early evolution of this dating facility was described previously (Suter et al, 1981a,b). This paper is a brief report on the current status of the system and its development.
The ETH/SIN AMS dating facility is routinely used for 10Be, 14C, 26Al, and 36Cl measurements. The present status and performance of this facility are reviewed and some of its major applications summarized.
10Be (T1/2 = 1.5·106y) is mainly produced in the atmosphere by cosmic ray spallation reactions on nitrogen and oxygen. About 70 % of the production takes place in the stratosphere. 10Be becomes attached to aerosols within a very short time. If 10Be is produced in the stratosphere some latitudinal mixing occurs. Most of the 10Be is transferred to the troposphere during spring and early summer when, mainly at median latitudes, large stratospheric air masses enter the troposphere. Tropospheric 10Be is deposited rapidly on the earth's surface by precipitation. The mean residence time of 10Be in the atmosphere is ca 1 to 2 years. 10Be removed from the atmosphere by precipitation is either preserved in snow and ice layers, in the topsoil and the biosphere, or it enters the hydrosphere (oceans and lakes), where it is transported to the sediments.